Question: What is the period of $y=\cos(-4\pi x+3)-7$ ? Give an exact value. units
Period in sinusoids of the form $y=a\cos(bx+c)+d$ Graphically, the period of a sinusoidal function is the horizontal distance between the ends of a single cycle of its graph. The period of a sinusoid of the form $y={a}\cos( bx + c) + {d}$ is equal to $\dfrac{2\pi}{| b|}$. [How can we justify this given our graphical understanding of period?] Finding the period The period of $y=\cos({-4\pi} x+3)-7$ is: $\begin{aligned} \text{period}&=\dfrac{2\pi}{|{b}|}\\\\ &=\dfrac{2\pi}{|{-4\pi}|} \\\\\\\\\\ &= \dfrac{1}{2} \\ \end{aligned}$ The answer The period of $y=\cos(-4\pi x+3)-7$ is $\dfrac12$ units.